In “Why Voter ID Laws Don’t Swing Many Elections,” Nate Cohn understates the impact of restrictive voting laws. Yes, it is likely rare for an election to be close enough for voter ID laws to swing the outcome. But Americans should indeed be concerned about laws that shut out thousands of eligible voters.

Cohn says “figures overstate the number of voters who truly lack identification.” But the evidence underlying these figures is quite strong and detailed.

Consider Texas, where U.S. District Judge Nelva Gonzales Ramos relied on such figures to strike down the strictest photo ID law in the country. The trial court found approximately 608,470 registered Texas voters lack the ID necessary to vote. This number was based on the research of two leadingpolitical scientists who compared Texas’s voter registration records to identification database records: Stephen Ansolabehere, PhD, a professor of government at Harvard University, and Michael C. Herron, PhD, chair of the math and social science department and a professor of government at Dartmouth College.

Cohn writes that if such an analysis were conducted in his hometown of Washington, D.C., he would erroneously be included in a tally of voters lacking photo ID, because he has a U.S. passport, not a D.C.-issued ID. But experts in the Texas case explicitly looked for these voters and excluded them from the count.

Under the Texas law, a voter must present one of seven forms of photo ID to vote: four are issued by Texas and three by the federal government. The Texas matching analysis reviewed state databases to determine whether registered voters had a Texas-issued photo ID, and also compared the state’s list of registered voters to multiple federal databases to capture people who may have a passport, military ID, or citizenship certificate instead. This means the approximately 608,470 registered Texans the court found lack ID don’t have any ID — state or federal — that can be used to vote.

The records-matching process in the Texas trial also took additional measures to ensure the accuracy of the data. The analysis used 13 separate identifiers to match registered voters with all of the acceptable forms of ID, including data related to date of birth, gender, first, middle, and last names, social security number, and driver’s license number. The comparisons were run multiple times using various combinations of these identifiers, and if any one combination resulted in a match between a voter registration record and an ID record, that person was assumed to own accepted photo ID.

Under this analysis, if Cohn were a Texas resident who registered under “Nate” but had a qualifying government-issued photo ID with “Nathan,” he would not have been counted among the 600,000-plus voters lacking ID. The matching procedure was designed to err on the side of over-matching, so as to provide a conservative estimate of the number of voters lacking ID.

Two additional experts at trial — Matt Barreto, PhD, professor at the University of Washington, and Gabriel Sanchez, PhD, professor at the University of New Mexico — conducted a detailed telephone survey of thousands of Texans to find out what forms of ID they possess. Unlike the matching procedure discussed above, the survey was not limited to registered voters, but was designed to determine how many eligible voters lack any form of ID used to vote under the law. The results: Approximately 1.2 million eligible Texas voters lack accepted ID.

Although the case in Texas has an especially detailed factual record, these studies do not stand alone. Numbers from other states show similar impact. In Wisconsin, a federal court found approximately 300,000 registered voters lack photo ID. In reaching that number, the court considered individuals who don’t possess a state-issued ID but may have another photo ID accepted for voting. In Pennsylvania, where the photo ID law was struck down this year, the state’s own witness estimated 320,000 to 400,000 registered voters lacked accepted ID. And a North Carolina analysis found more than 300,000 voters lack ID. More data will come to light when North Carolina’s law goes on trial in July 2015. In the meantime, we should be careful not to conflate preliminary studies with those that have been subject to judicial scrutiny and formed the basis for court findings, such as those in Texas, Pennsylvania, and Wisconsin. These numbers are further supported by national survey data from multiple sources showing 11 percent of Americans lack the kind of government-issued photo ID required by strict ID laws.

In the face of mounting evidence of voter ID’s disenfranchising effects, Judge Richard Posner — a leading conservative jurist who wrote the pivotal appellate court opinion upholding Indiana’s strict photo ID law a decade ago — reversed course and come out against voter ID laws. In a book released last year, Posner wrote that ID laws are “widely regarded as a means of voter suppression.”

Cohn also took issue with the argument that voter ID laws affect turnout. He is correct that changes in turnout often result from a number of factors, and the impact of any one factor on voter participation in a given election is difficult to assess. However, the Government Accountability Office, a respected nonpartisan institute, recently issued a study showing Kansas and Tennessee’s new photo ID laws decreased turnout in 2012 by 2 to 3 percent.

Voter ID laws present a threat to democracy because they stop individuals — like Ms. Sammie Louise Bates, Mr. Eulalio Mendez, Jr., Mr. Calvin Carrier, and many more — from exercising their right to vote. The numbers from the Texas photo ID case and other states illustrate the extent of this threat — and why it is wrong to pass laws that block some eligible Americans from voting.